Non-Hermitian-induced higher-order topological phases in acoustic fractal lattices

TL;DR

This paper demonstrates how non-Hermitian effects, specifically loss contrast, can induce and control higher-order topological states in acoustic fractal lattices, revealing new topological phenomena in non-integer dimensions.

Contribution

It introduces a novel non-Hermitian approach to realize and manipulate higher-order topological phases in acoustic fractal lattices without changing the lattice structure.

Findings

Experimental observation of topological edge and corner states.

Loss contrast tuning alters energy localization.

Theoretical framework for non-Hermitian topological states in fractals.

Abstract

Non-Hermitian systems enable continuous and smooth tuning of topological phases through externally controllable loss/gain parameters. Without altering the intrinsic lattice structure, merely fine-tuning the intensity or spatial distribution of the loss or gain can induce the emergence of higher-order topological states, and even achieve reversible switching of topological phases. However, in non-integer dimensions, topological states induced by non-Hermiticity remain unexplored, which hinders the continuous and smooth manipulation of systems with rich higher-order topological states. By introducing a loss contrast in a fractal lattice, this study proposes a non-Hermitian route to realize higher-order topological phases in acoustic fractal lattices. Based on the tight-binding approximation, calculating the Hamiltonian of the system yields the wave-function distribution of the zero-energy modes, revealing the formation mechanisms and conditions for the topological phase transitions induced by non-Hermiticity in acoustic fractal lattices. We numerically and experimentally realize non-Hermitian-induced topological edge and corner states in a fractal structure. Furthermore, theoretical and numerical results demonstrate that merely adjusting the loss contrast can alter the degree of energy localization. This work not only establishes an effective mechanism for manipulating higher-order topology in complex fractal geometries through non-Hermiticity but also provides a theoretical framework for exploring exotic topological states of matter in non-integer dimensions.